Scott Arfield had Falkirk's best efforts with the visitors still in search of a first SPL win this season. David Obua met Lee Wallace's cross but could not divert his header on target in an early Hearts attack.
Kjartan Finnbogason may have done better when presented with a chance in the box following a mistake by Ismael Bouzid but the Icelandic striker took too long and goalkeeper Janos Balogh was able to smother the ball.
Nade then fired over before Driver missed an excellent chance to open the scoring 10 minutes before half-time. The winger combined with Suso and raced clear of the Bairns defence but shot beyond the frame of Olejnik's goal from a promising position.
At the other end, Alex MacDonald's long-range effort troubled Balogh as it skidded off the wet surface. Falkirk captain Darren Barr was shown a yellow card after pulling down Suso on the edge of the box with referee Chris Boyle judging that Barr had not denied a clear scoring opportunity.
An Arfield 18-yard shot flashed wide of the Hearts goal as the first half drew to a close.
The visitors continued to press at the start of the second half and Jose Goncalves made an important block from Ryan Flynn's shot. Balogh then saved another effort from Arfield. Finnbogason failed to connect properly with MacDonald's cut-back and Danijel Marceta could not convert when the ball fell loose.
Suso showed skill to set up Michael Stewart for a shot 25 yards from goal but the Hearts skipper could not find the target. Olejnik then made a comfortable save from Suso before Stewart left the pitch to jeers from the home fans as he was replaced by Ian Black in the 77th minute.
A long throw-in by Goncalves was flicked on by the head of McLean towards goal but Olejnik was alert to keep the scores level. David Witteveen had earlier replaced Nade and the Austrian went through on goal late in the match only to be foiled by McLean's last-ditch tackle.
Hearts manager Csaba Laszlo said "It's not the best result for us and with the chances we created we could have been 5-0 ahead. "I can't always defend players and say they need time. In professional football you don't have a lot of time. We need the fans to support us. "If you don't score goals then you don't win games. How many teams can create five or six chances in a game?"